In standard electronic systems, resonator oscillators are designed by using the known negative-impedance structure, such as is described for example, in the PhD thesis entitled ‘Design of High-Performance Negative-Feedback Oscillators’ by C. A. M. Boon and in the paper entitled ‘Low-Noise Oscillators’ published in ‘Analog Circuit Design’ by J. H. Huijsing et al., Kluwer Academic Publishers 1996. Selection of the desired resonance mode of a resonator is usually done using tuned circuits to enable discrimination of the different modes in the frequency domain.
Referring now to FIG. 1, there is shown an electrical model of two single resonance-mode resonators in the prior art. FIG. 1 depicts both a series and a parallel resonator, having a resonance frequency ω0:
            ω              0        ,        s              =          1                                    L            s                    ⁢                      C            s                                          ω              0        ,        p              =          1                                    L            p                    ⁢                      C            p                              for the series resonator, andfor the parallel resonator.
In case of a series resonance the impedance is very low at resonance, while in the parallel resonator the impedance is very high at resonance. In both resonators, the impedance at resonance is purely resistive and given by:Z(ω0)series=RsZ(ω0)parallel=Qp2RsThe quality factor Qp is given by:
      Q    p    =            ω      0        ⁢                  L        p                    R        s            
It is well known in the prior art that to construct an oscillator with this kind of resonator, the losses that are present in the resistive element have to be counteracted to sustain oscillation. This is typically accomplished by connecting the resonator to an amplifier that behaves like a negative resistance. This circuit will supply the energy that is lost during each cycle to sustain oscillation. Amplitude control of the oscillation can be performed by adjusting the value of the negative impedance circuit.
In multi-mode resonators, more than one parallel or series resonance modes is present, of which usually only one is the desired mode. A well known and often used example of the multi-mode resonator is the overtone crystal resonator. In a prior art crystal resonator, the first overtone, or fundamental is established when the crystal is resonating in its ground harmonic frequency. Although every crystal can be excited to resonate in an (odd) overtone like 3rd 5th or 7th overtone, crystal manufacturers usually provide crystals that are specifically cut for this purpose.
Overtone crystal oscillators usually use a crystal specifically intended to be used as an overtone resonator, together with the negative impedance circuit and an extra frequency selective (tuned) circuit to select the desired overtone as shown in FIG. 2.
Other examples of multi-mode resonators include micro-machined structures that are specifically intended for this purpose, like micro-machined accellerometers.
In U.S. Pat. No. 6,225,872 a method of selecting a desired resonance mode in the time domain is introduced, using a synchronized first-order, or relaxation oscillator as the time-selective element. The prior art patent describes how a first-order, or relaxation oscillator can be used to select a resonance mode in a resonator using selectivity in the time domain. It is described how the square wave output of a first-order oscillator, oscillating at frequency ω1 is fed into a multi-mode resonator as shown in FIG. 3. When the frequency ω1 is close to the desired resonance at frequency ω0 of the multi-mode resonator, the desired resonance will be excited. The sine-wave at the output of the multi-mode resonator can be used to synchronize the first-order oscillator, enabling sustained oscillation at coo.
Referring now to FIG. 4, there is shown how reference levels El and Eh in the prior art circuit are modulated with the amplified output of the multi-mode resonator in order to make the first-order oscillator lock to the desired resonance mode of the multi-mode resonator. When the oscillator is locked, the first-order oscillation is in complete lock with the desired resonance mode, as shown in FIG. 5.
There are several disadvantages with this prior art oscillator. One problem of the first-order oscillator of the prior art is that it always excites the multi-mode resonator with a square or sawtooth shaped waveform. However, when high spectral purity is required, it is advantageous for the multi-mode resonator to be excited by a sine wave. To enable locking, a required feature of an oscillator implementing the timing reference is the ability to perform an instantaneous phase reset when synchronized to an external signal. Therefore, in oscillators having a high spectral purity from a multi-mode resonator, without the need for (external) tuning circuits, the need exists for a system in which an oscillator is implemented using a sine-wave oscillator with resettable phase.